1028 science project ideas, from class 1 to college.

What it shows

Beads falling through seven rows of nails bounce left or right at random at each nail. With eight collecting slots at the bottom, the expected share of beads in each slot follows Pascal's triangle, 1, 7, 21, 35, 35, 21, 7, 1 out of 128, which draws a bell-shaped curve.

You will need

• A plywood board 30 cm by 45 cm
• 28 small nails in a triangle of seven staggered rows
• Thin card strips for eight collecting channels
• A clear plastic sheet from an old folder as the front
• About 200 mustard seeds or 5 mm beads
• A funnel at the top
• Tape and glue

Safety: An adult must hammer the nails and check none pokes through the back.

Take it further: Bend some nails so beads go right with probability more than a half, and show the peak shifting to one side like a skewed distribution.

What it shows

In a group of just 23 people there is a better than even chance (about 50.7 percent) that two share a birthday, and with 30 people the chance is about 70.6 percent. Collecting birthdays from many class sections shows how often a shared birthday actually turns up.

You will need

• Permission from the school to collect day and month of birth only, no year or names
• A survey sheet for each section
• A calculator or a spreadsheet
• Chart paper for the results

Take it further: Work out how many people are needed for a 50 percent chance that someone shares your own birthday: it is 253, far more than 23.

What it shows

Equal weights hung from a numbered beam at the data values balance only when the support is at the mean. Weights at 2, 3 and 7 balance at 4, their mean, and moving one weight from 7 to 13 shifts the balance point to 6, showing how an extreme value pulls the mean.

You will need

• A straight wooden scale or a 60 cm batten marked 0 to 20
• A triangular block or a pencil fixed to a base as the pivot
• Six identical washers or coins with thread loops
• A nail or hook at every number mark
• A small level or a straight edge

Safety: An adult must fix the hooks and make sure the beam cannot fall on fingers.

Take it further: Hang two washers at one value to show frequency, and find the mean of a frequency table on the beam.

What it shows

Paper cups stacked in a triangle carry Pascal's numbers: each cup holds the sum of the two cups above it. Row sums double each time (1, 2, 4, 8, 16, 32), the second diagonal counts 1, 2, 3, 4, and the third diagonal holds the triangular numbers 1, 3, 6, 10, 15.

You will need

• 55 paper cups for ten rows
• A marker
• Coloured stickers for odd and even numbers
• A board or a wall space and tape
• A calculator to check the big numbers

Take it further: Read each row as a number (1, 11, 121, 1331, 14641) and show these are powers of 11 until carrying spoils it at row 5.

What it shows

Squares of side 1, 1, 2, 3, 5, 8 and 13 cm fit together into a rectangle of 13 cm by 21 cm, and a quarter circle in each square joins into a spiral. The ratio of the sides, 21 divided by 13, is about 1.615, close to the golden ratio 1.618, and the ratio gets closer as more squares are added.

You will need

• Chart paper and coloured paper
• A compass, ruler and set square
• Scissors and glue
• A calculator
• A board 30 cm by 40 cm

Safety: Keep the compass point capped when not in use.

Take it further: Measure the ratio of your height to the height of your navel and of several objects in the room, and see which come near 1.6.

What it shows

Rice grains scattered evenly over a square land inside the circle drawn within it with probability equal to the circle's share of the area, which is pi divided by 4. Counting grains inside and outside and multiplying the inside fraction by 4 estimates pi, a Monte Carlo method used in real computer simulations.

You will need

• A square tray or a 30 cm square drawn on chart paper with a tape border
• A compass to draw the largest circle inside the square
• About 500 grains of rice or mustard seeds
• A tally sheet and a calculator
• A sieve or a sheet to scatter grains from a height

Take it further: Write a ten-line program that drops a million random points and compare its estimate with your rice result.

What it shows

Square tiles of side x, strips of x by 1 and unit squares are arranged into a rectangle. One x squared tile, five x strips and six unit tiles fit exactly into a rectangle with sides x + 2 and x + 3, so x squared + 5x + 6 = (x + 2)(x + 3).

You will need

• Thick cardboard or foam sheet in three colours
• A ruler and cutter
• A board with a right-angled corner frame
• Labels for x squared, x and 1
• A box to hold the tile set

Safety: An adult must cut the tiles with the cutter.

Take it further: Make red tiles for negative terms and factorise x squared take away x take away 6 as (x take away 3)(x + 2).

What it shows

Pins at grid points on a four-quadrant board let a string be stretched through any two points to show a straight line. The string through (0, 1) and (2, 5) rises 4 for every 2 across, slope 2, and crosses the y axis at 1, so its equation is y = 2x + 1.

You will need

• A cork sheet or soft board 40 cm square
• Centimetre graph paper with axes from minus 10 to 10
• A box of drawing pins
• Coloured thread or elastic
• Labels and a marker
• A set square for perpendicular lines

Safety: Drawing pins are sharp; store them in a closed tin and keep the board out of reach of small children.

Take it further: Pin the three vertices of a triangle and use the coordinates to find its area with the shoelace formula, then check by counting squares.

What it shows

Two players take 1, 2 or 3 sticks in turn from a pile of 21 and the player who takes the last stick wins. Whoever leaves a multiple of 4 after their move (20, 16, 12, 8, 4) can always win, so the second player wins a game of 21 by always making the two moves in a round add to 4.

You will need

• 21 matchsticks, straws or pencils
• A board marked with 21 slots
• A score sheet
• Two players and a referee

Safety: Use burnt matchsticks or straws so there is nothing to strike.

Take it further: Study the three-pile version of Nim and find the rule that uses binary addition without carrying.

What it shows

Discs of different sizes must be moved from one peg to another, one at a time, never putting a larger disc on a smaller one. The least number of moves is 1, 3, 7, 15, 31 and 63 for 1 to 6 discs, which is 2 to the power n minus 1, so 64 discs would take more than 18 quintillion moves.

You will need

• Six lids or caps of clearly different sizes, from a bottle cap to a jar lid
• Three pegs: pencils stuck upright in a plank or clay base
• A stopwatch
• A record sheet

Safety: An adult must fix the pegs; blunt the pencil tops.

Take it further: Write a short program or a flowchart for the recursive solution and let it print the moves for 4 discs.

What it shows

In any year the dates 4/4, 6/6, 8/8, 10/10, 12/12, 9/5, 5/9, 7/11, 11/7 and the last day of February all fall on the same weekday, called the doomsday. A wheel finds the doomsday for the year, and counting from the nearest of these dates gives the weekday of any date, such as 15 August 1947, a Friday.

You will need

• Two card circles, 20 cm and 14 cm, joined at the centre with a split pin
• A marker and ruler
• A list of the doomsday dates printed on the base
• A calculator to check
• An old calendar for testing

Safety: An adult must push the split pin through the card.

Take it further: Work out the weekday of your 50th birthday and of 26 January 1950, and show both with the wheel.

What it shows

To square a number ending in 5, multiply the tens digit by the next number up and write 25 after it: 35 squared is 3 times 4 = 12 followed by 25, so 1,225. The flip board shows each step and the algebra behind it: (10a + 5) squared = 100a(a + 1) + 25.

You will need

• A cardboard base 40 cm by 20 cm
• Flip cards on rings or tape hinges for the tens digit and the answer
• A marker
• A calculator for checking
• A small whiteboard sheet for visitors to try

Take it further: Make a board for squaring numbers near 50: 50 + d squared is 2,500 + 100d + d squared, so 53 squared is 2,809.

What it shows

To multiply 97 by 96, write how far each is below 100 (3 and 4). Subtract crosswise, 97 minus 4 = 93, and multiply the deficits, 3 times 4 = 12, to get 9,312. The slider lines up the two numbers and their deficits so the answer appears in two steps.

You will need

• A card strip 50 cm long with two sliding windows
• A number strip from 90 to 110
• A marker
• A calculator for checking
• Glue and a cutter

Safety: An adult must cut the windows in the card.

Take it further: Make a base-1,000 strip for numbers like 997 times 994, where the deficit product is written with three digits: 991,018.

What it shows

Threads joined between two scales at right angles, the first point on one to the last on the other and so on, form no curve themselves, yet their edges outline a smooth parabola. The curve is the envelope of the lines, touched by every one of them.

You will need

• A square of plywood or thick card 30 cm across
• 40 small nails or pins
• Coloured thread
• A ruler and pencil
• A hammer or a pushpin tool

Safety: An adult must hammer the nails and cover the points at the back with tape.

Take it further: Put nails round a circle and join each nail n to nail 2n to see a cardioid envelope appear.

What it shows

Four land areas joined by seven bridges cannot be walked in one trip crossing every bridge once, because every land area has an odd number of bridges. Lifting any one bridge off the board leaves only two odd areas and the walk becomes possible, starting at one odd area and ending at the other.

You will need

• A board painted as a river with two banks and two islands
• Seven removable card bridges with velcro or pegs
• A toy figure to walk the route
• A dry-erase sheet to draw the graph
• Labels A to D for the land areas

Take it further: Draw the map of your school corridors as a graph and find a route that walks every corridor exactly once, or prove there is none.